erweitern k^2((k^2+1)(k^2+2))/6+k^2+1

Lösung

erweitern

k^{2} \frac{( k ^{2} + 1 ) ( k ^{2} + 2 )}{6} + k^{2} + 1

\frac{k ^{6}}{6} + \frac{k ^{4}}{2} + \frac{k ^{2}}{3} + k^{2} + 1

Schritte zur Lösung

k^{2} \frac{( k ^{2} + 1 ) ( k ^{2} + 2 )}{6} + k^{2} + 1

k^{2} \frac{( k ^{2} + 1 ) ( k ^{2} + 2 )}{6} = \frac{k ^{6} + 3 k ^{4} + 2 k ^{2}}{6}

= \frac{k ^{6} + 3 k ^{4} + 2 k ^{2}}{6} + k^{2} + 1

Wende Bruchregel an:

\frac{a \pm b}{c} = \frac{a}{c} \pm \frac{b}{c}

\frac{k ^{6} + 3 k ^{4} + 2 k ^{2}}{6} = \frac{k ^{6}}{6} + \frac{3 k ^{4}}{6} + \frac{2 k ^{2}}{6}

= \frac{k ^{6}}{6} + \frac{3 k ^{4}}{6} + \frac{2 k ^{2}}{6} + k^{2} + 1

Streiche

\frac{3 k ^{4}}{6} : \frac{k ^{4}}{2}

= \frac{k ^{6}}{6} + \frac{k ^{4}}{2} + \frac{2 k ^{2}}{6} + k^{2} + 1

Streiche

\frac{2 k ^{2}}{6} : \frac{k ^{2}}{3}

= \frac{k ^{6}}{6} + \frac{k ^{4}}{2} + \frac{k ^{2}}{3} + k^{2} + 1

e x p an d (1 + \frac{a x}{3})^{4}

e x p an d \frac{3 + sin ( 2 x )}{( 3 + tan ( x ) ) ^{2}}

e x p an d \frac{4}{π} (cos (3 t) - sin (5 t))

e x p an d (- sec (t) tan (t) + sin (t))^{2}

e x p an d 3 x (x^{2} - 3 x)